Conventionally, it has been known to use a surface light source device using plural light-emitting diodes (hereafter, referred to as “LED,” as appropriate) as lighting means for irradiating a liquid crystal display monitor for use in a personal computer, a television, and the like. The surface light source device has the plural light-emitting diodes provided in a matrix manner in a tabular region having substantially the same shape as a liquid crystal display panel of the liquid crystal display monitor. The surface light source device performs planar irradiation to the liquid crystal display monitor from a back surface side of the liquid crystal display monitor, with light from the light-emitting elements. In the surface light source device, a brightness distribution of which light has been made substantially uniform by the light flux controlling member.
An example of the lighting device using LED as the light source is a lighting device 100 disclosed in Patent document 1. FIG. 19 is a cross-sectional view of the conventional lighting device 100. The lighting device 100 includes a light-emitting element 101 on a backside surface 102c and also a light flux controlling member 102 around the light-emitting element 101 that changes a direction of light emitted from the light-emitting elements 101. A liquid crystal display panel 106 is provided above the lighting device 100. The lighting device 100 is arranged such that the light from the light flux controlling member 102 is incident on the liquid crystal display panel 106 with a substantially even brightness distribution.
Specifically, the light flux controlling member 102 has a shape in which (i) angles φ1 and φ2 satisfy a formula of φ2/φ1>1 and (ii) a value obtained by the formula gradually decreases as φ1 increases, where: the angle φ1 is an angle between a light axis Z and the light emitted from the light-emitting element 101, entering a light incoming surface 102a of the light flux controlling member 102, and reaching a light outgoing surface 102b of the light flux controlling member 102; and the angle φ2 is an angle between the light axis Z and light L emitted from the light outgoing surface 102b. 
By arranging the light outgoing surface 102b as described above, it is possible to smoothly broaden a light flux of the light emitted from the light-emitting element 101 over a wide range of the liquid crystal display panel 106. That is, light from the light-emitting elements 101 becomes readily blendable when a plurality of the light-emitting elements 101 are used as light sources. Thus, (i) even if there are variations in emission colors from the light-emitting elements 101, such variations are less detectable after being emitted via the light flux controlling member 102 and (ii) a brightness of the outgoing light becomes uniform. This allows realizing a surface light source device of high quality.
Another example of the light-emitting device using the LED as the light source is a light-emitting device disclosed in Patent document 2.
The lighting device in the Patent document 2 is arranged such that a light flux controlling member is formed by a bottom surface, a first surrounding curved surface extending from the bottom surface, and a first inner curved surface extending from the first surrounding curved surface, wherein a distance from a center of the bottom surface to an arbitrary point on the first inner curved surface is shorter than a radius of curvature at the arbitrary point on the first central curved surface. By arranging the first inner curved surface as described above, it is possible to broaden a light flux of light emitted from a light-emitting element over a wide range of a liquid crystal panel.
The lighting device in the Patent document 2 further has an empty space in the center of the bottom surface. Internal surfaces of the empty space are formed of a second surrounding curved surface and a second inner curved surface, wherein a distance from the center of the bottom surface to an arbitrary point on the second inner curved surface is longer than a radius of curvature at the arbitrary point on the second inner curved surface. By arranging the second inner curved surface as described above, it is possible to broaden the light flux of the light from the light-emitting element over the wide range of the liquid crystal panel.
The lighting device in the Patent document 2 further includes a conical recession at the center of the first inner curved surface such that the light flux, emitted from the light-emitting element into a direction more parallel to a light axis direction, is refracted into a direction away from the light axis direction.
(Patent Document 1)
Japanese Unexamined Patent Publication No. 2006-92983 (Tokukai 2006-92983) (published on Apr. 6, 2006)
(Patent Document 2)
Japanese Unexamined Patent Publication No. 2006-114863 (Tokukai 2006-114863) (published on Apr. 27, 2006)
However, the aforesaid conventional lighting devices cause the following problems, respectively.
In the light-emitting device 100 disclosed in the Patent document 1, the light flux controlling member 102 requires to have higher scattering ability, as a distance from the light-emitting element 101 to the liquid crystal display panel 106 becomes shorter or as a distance from the light-emitting element 101 to a neighboring light-emitting element becomes longer.
In order to improve the scattering ability of the light flux controlling member 102, it is necessary that the light emitted from the light-emitting elements 101 reach a position away from an area directly above the light-emitting elements 101, on the liquid crystal display panel 106. In order to obtain such light, it is necessary to refract the outgoing light as parallel to the liquid crystal display panel 106 as possible, on the light outgoing surface 102b. That is, it is necessary to significantly refract the light, on the light outgoing surface 102b. However, significant light refraction by the light outgoing surface 102b generally increases a reflex amount, due to a phenomenon called the Fresnel's reflection. That is, an amount of the light emitted from the light outgoing surface 102b decreases. In particular, the Fresnel's reflection effect becomes significant in the light-emitting device 100 disclosed in the Patent document 1 since the light-emitting device 100 is arranged such that control of the light direction is mainly performed at the light outgoing surface 102b, thereby having a need for further significantly refracting the light on the light outgoing surface 102b so that the higher scattering ability is obtained.
Furthermore, as shown by the arrow direction indicated by the dished line in FIG. 19, the light thus reflected on the light outgoing surface 102b is then reflected by a backside surface 102c of the light flux controlling member 102 or by a reflecting member 103 arranged in contact with the backside surface 102c. Then, the light is condensed in the vicinity of the area directly above the light-emitting element 101. As a result of the above, even if the refraction angle is set larger so as to obtain the higher light scattering ability of the light flux controlling member 102, (i) the amount of the light arranged to reach the position away from the area directly above the light-emitting element decreases after all, and (ii) the light is condensed in the area directly above the light-emitting element 101. As such, it becomes harder to obtain the higher scattering ability.
Furthermore, the Patent document 1 discloses the following as to the arrangement of the light flux controlling member 102: where (i) δ1 is a constant value of not more than π/2 and (ii) α is a coefficient of scattering ability of the light flux controlling member 102, a relation between φ1 and φ2 is expressed by a relation expression of φ2=(1+(δ1−φ1)×α/δ1)×1.
FIG. 20 is a graph showing the relation between the angles φ1 and φ2 of the light emitting device 100. As shown in FIG. 20, when scattering ability larger than that of the light-emitting device 100 disclosed in Embodiment of the Patent document 1 is required, a region where the angle φ1 is relatively small has a region where an increase of the angle φ1 does not change the φ2 
FIG. 21 illustrates a direction of emission expressed by the relational equation in FIG. 20. In the region shown in FIG. 20 where the increase of the φ1 does not change the φ2, (i) the directions of emission overlap each other and (ii) the outgoing light fluxes are concentrated, as shown in FIG. 21, thereby causing a bright line of a ring-shape. Thus, uneven brightness is generated. In order to prevent the generation of such uneven brightness, it is necessary to use the light flux controlling member 102 having α<1. However, under such a requirement, there may be a case where the light-emitting device 100 is unsatisfactory in the view of obtaining the higher scattering ability. That is, there may be a case where it is unsatisfactory, in the view of obtaining the larger scattering ability, to simply form the light flux controlling member in the shape in which the value of the φ2/φ1 gradually decreases as φ1 increases.
In the light-emitting device disclosed in the Patent document 2, the radius of curvature is significantly changed at an interface of the first inner curved surface and the first surrounding curved surface such that the light is refracted toward the light axis on the surrounding curved surface. As a result, the light emitted in the vicinity of the interface is condensed, thereby resulting in the generation of the ring-shaped bright line. In order to prevent the generation of the bright line, it is proposed in an Embodiment to use a type of a light-emitting device that does not have the first surrounding curved surface. However, this arrangement has a lens that is remarkably large, thus not being practical. The reason of this can be explained as follows. The lens becomes larger in an arrangement in which a distance from a center of a bottom surface to an arbitrary point on a first inner curved surface is set shorter than a radius of a curvature at the arbitrary point on the first inner curved surface. As such, a first surrounding curved surface is necessary to be provided.
Furthermore, it is described in the Patent document 2 that the lighting device may have a first surrounding curved surface, an inner curved surface, and a most-inner curved surface. However, the most-inner curved surface has conical geometry, thereby refracting, into a direction away from the light axis, light emitted in a light axis direction from the center of a bottom surface. In this case, it gets darker on the light axes of the light flux controlling members, causing spot-like uneven brightness. Thus, with the invention disclosed in the patent document 2, it is difficult to prevent the uneven brightness, though it is possible to scatter the light with the invention.